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How big should asteroids be to

  1. Nov 8, 2009 #1
    Consider main-belt chondritic asteroids. How large should be an asteroid so that the
    maximal internal temperature exceeds the melting temperature of ice? Of rocks? For your
    calculations, use the present-day chondritic heat production w = 4×10-12 W kg-1, typical
    thermal conductivity of slightly fractured rock k = 2 W K-1m-1, and density r = 2700 kg
    m-3 representative of chondritic materials. Make (and explain) a reasonable guess about
    the surface temperature Ts and melting temperatures Tm of ice and rocks
     
  2. jcsd
  3. Nov 8, 2009 #2

    mgb_phys

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    Welcome to PF - you have to show some attempt to work out the homework before we can help.
     
  4. Nov 8, 2009 #3
    well i know heat flux = -k(dt/dr) this is change in temperature with depth and thermal diffusivity x= k/pC (here p is density and C is heat capacity). I just don't know how to apply heat production. I feel like i'm missing an equation and i have no idea what it is.
     
  5. Nov 8, 2009 #4

    mgb_phys

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    Heat production is given per mass, so with the density it's easy to work out heat production/volume. If you assume a spherical asteroid you can get a heat prouction / radius relation
     
  6. Nov 8, 2009 #5
    the units for that would be W/m^3. this is almost heat flux (W/m^2). where would i go from there?
     
  7. Nov 9, 2009 #6
    asteroid size

    How large should be the body so that the maximal internal temperature reaches given
    temperature Tm (melting temperature)?

    I'm thinking i can use F= K*[(Ta-Tb)/(Ra-Rb)]. where F is heat flux, K is thermal conductivity, T is change in temperature and R is change in depth.
    I'm thinking the radius i need should be R=(K*(Tm))/F, but i'm not sure if it is that easy.

    I need some reassurance.

    Thank you
     
  8. Nov 9, 2009 #7

    berkeman

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    (two threads on the same question merged into one)

    (thread moved to Advanced Physics Homework Help)
     
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